Input Data Set
| Input Data Set | |
|---|---|
| Name | WORK.PREPROCESSEDDATA |
| Time ID Variable | Date_of_death |
| Input Data Set | |
|---|---|
| Name | WORK.PREPROCESSEDDATA |
| Time ID Variable | Date_of_death |
| Estimation Span Summary | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Variable | Type | First Obs | Last Obs | NObs | NMiss | Min | Max | Mean | Standard Deviation |
| incidents | Dependent | FEB2000 | SEP2019 | 236 | 0 | 1.00000 | 4.00000 | 2.40678 | 1.30620 |
| Forecast Span Summary | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Variable | Type | First Obs | Last Obs | NObs | NMiss | Min | Max | Mean | Standard Deviation |
| incidents | Dependent | FEB2000 | SEP2019 | 236 | 0 | 1.00000 | 4.00000 | 2.40678 | 1.30620 |
| Preliminary Estimates of the Free Parameters | ||
|---|---|---|
| Component | Parameter | Estimate |
| Irregular | Error Variance | 1.35915 |
| Level | Error Variance | 0.50968 |
| Season | Error Variance | 1.78570 |
| Likelihood Based Fit Statistics | |
|---|---|
| Statistic | Value |
| Full Log Likelihood | -395 |
| Diffuse Part of Log Likelihood | -2.485 |
| Non-Missing Observations Used | 236 |
| Estimated Parameters | 3 |
| Initialized Diffuse State Elements | 12 |
| Normalized Residual Sum of Squares | 224 |
| AIC (smaller is better) | 796.06 |
| BIC (smaller is better) | 806.29 |
| AICC (smaller is better) | 796.17 |
| HQIC (smaller is better) | 800.19 |
| CAIC (smaller is better) | 809.29 |
| Likelihood Optimization Algorithm Converged in 15 Iterations. |
| Final Estimates of the Free Parameters | |||||
|---|---|---|---|---|---|
| Component | Parameter | Estimate | Approx Std Error |
t Value | Approx Pr > |t| |
| Irregular | Error Variance | 1.63668 | 0.15598 | 10.49 | <.0001 |
| Level | Error Variance | 0.00097308 | 0.0011333 | 0.86 | 0.3905 |
| Season | Error Variance | 1.851008E-7 | 0.0001057 | 0.00 | 0.9986 |
| Fit Statistics Based on Residuals | |
|---|---|
| Number of non-missing residuals used for computing the fit statistics = 224 | |
| Mean Squared Error | 1.99422 |
| Root Mean Squared Error | 1.41217 |
| Mean Absolute Percentage Error | 76.15010 |
| Maximum Percent Error | 75.24209 |
| R-Square | -0.19127 |
| Adjusted R-Square | -0.20205 |
| Random Walk R-Square | 0.32623 |
| Amemiya's Adjusted R-Square | -0.22361 |
| Significance Analysis of Components (Based on the Final State) | |||
|---|---|---|---|
| Component | DF | Chi-Square | Pr > ChiSq |
| Irregular | 1 | 7.70 | 0.0055 |
| Level | 1 | 109.66 | <.0001 |
| Season | 11 | 13.62 | 0.2550 |
| Trend Information (Based on the Final State) | ||
|---|---|---|
| Name | Estimate | Standard Error |
| Level | 2.080551539 | 0.1986823 |
| Summary of Seasons | |||
|---|---|---|---|
| Name | Type | Season Length | Error Variance |
| Season | DUMMY | 12 | 1.851008E-7 |
| Outlier Summary | |||||||
|---|---|---|---|---|---|---|---|
| Obs | Date_of_death | Break Type | Estimate | Standard Error |
Chi-Square | DF | Pr > ChiSq |
| 193 | FEB2016 | Additive Outlier | 2.63569 | 1.3192695 | 3.99 | 1 | 0.0457 |
| Forecasts for Variable incidents | |||||
|---|---|---|---|---|---|
| Obs | Date_of_death | Forecast | Standard Error |
95% Confidence Limits | |
| 237 | OCT2019 | 2.194152 | 1.32580 | -0.404372 | 4.792675 |
| 238 | NOV2019 | 2.512591 | 1.32605 | -0.086424 | 5.111605 |
| 239 | DEC2019 | 2.199461 | 1.32630 | -0.400041 | 4.798962 |
| 240 | JAN2020 | 1.675808 | 1.32655 | -0.924176 | 4.275792 |
| 241 | FEB2020 | 1.364240 | 1.32542 | -1.233526 | 3.962007 |
| 242 | MAR2020 | 2.416760 | 1.32566 | -0.181481 | 5.015001 |
| 243 | APR2020 | 2.219292 | 1.32590 | -0.379420 | 4.818003 |
| 244 | MAY2020 | 2.171808 | 1.32614 | -0.427370 | 4.770986 |
| 245 | JUN2020 | 2.324344 | 1.32637 | -0.275296 | 4.923985 |
| 246 | JUL2020 | 1.976857 | 1.32661 | -0.623242 | 4.576957 |
| 247 | AUG2020 | 1.979393 | 1.32684 | -0.621161 | 4.579947 |
| 248 | SEP2020 | 1.931914 | 1.32707 | -0.669091 | 4.532918 |
| Estimation Span Summary | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Variable | Type | First Obs | Last Obs | NObs | NMiss | Min | Max | Mean | Standard Deviation |
| incidents | Dependent | FEB2000 | OCT2019 | 237 | 0 | 1.00000 | 6.00000 | 2.85654 | 1.96271 |
| Forecast Span Summary | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Variable | Type | First Obs | Last Obs | NObs | NMiss | Min | Max | Mean | Standard Deviation |
| incidents | Dependent | FEB2000 | OCT2019 | 237 | 0 | 1.00000 | 6.00000 | 2.85654 | 1.96271 |
| Preliminary Estimates of the Free Parameters | ||
|---|---|---|
| Component | Parameter | Estimate |
| Irregular | Error Variance | 3.06877 |
| Level | Error Variance | 1.15079 |
| Season | Error Variance | 3.80885 |
| Likelihood Based Fit Statistics | |
|---|---|
| Statistic | Value |
| Full Log Likelihood | -491.2 |
| Diffuse Part of Log Likelihood | -2.485 |
| Non-Missing Observations Used | 237 |
| Estimated Parameters | 3 |
| Initialized Diffuse State Elements | 12 |
| Normalized Residual Sum of Squares | 225 |
| AIC (smaller is better) | 988.42 |
| BIC (smaller is better) | 998.66 |
| AICC (smaller is better) | 988.52 |
| HQIC (smaller is better) | 992.55 |
| CAIC (smaller is better) | 1001.7 |
| Likelihood Optimization Algorithm Converged in 13 Iterations. |
| Final Estimates of the Free Parameters | |||||
|---|---|---|---|---|---|
| Component | Parameter | Estimate | Approx Std Error |
t Value | Approx Pr > |t| |
| Irregular | Error Variance | 3.81662 | 0.36440 | 10.47 | <.0001 |
| Level | Error Variance | 0.00098475 | 0.0023703 | 0.42 | 0.6778 |
| Season | Error Variance | 4.033745E-8 | 0.00002663 | 0.00 | 0.9988 |
| Fit Statistics Based on Residuals | |
|---|---|
| Number of non-missing residuals used for computing the fit statistics = 225 | |
| Mean Squared Error | 4.58835 |
| Root Mean Squared Error | 2.14204 |
| Mean Absolute Percentage Error | 89.25113 |
| Maximum Percent Error | 83.33333 |
| R-Square | -0.20709 |
| Adjusted R-Square | -0.21796 |
| Random Walk R-Square | 0.33433 |
| Amemiya's Adjusted R-Square | -0.23971 |
| Significance Analysis of Components (Based on the Final State) | |||
|---|---|---|---|
| Component | DF | Chi-Square | Pr > ChiSq |
| Irregular | 1 | 8.74 | 0.0031 |
| Level | 1 | 156.71 | <.0001 |
| Season | 11 | 11.05 | 0.4393 |
| Trend Information (Based on the Final State) | ||
|---|---|---|
| Name | Estimate | Standard Error |
| Level | 3.089934955 | 0.2468335 |
| Summary of Seasons | |||
|---|---|---|---|
| Name | Type | Season Length | Error Variance |
| Season | DUMMY | 12 | 4.033745E-8 |
| Outlier Summary | |||||||
|---|---|---|---|---|---|---|---|
| Obs | Date_of_death | Break Type | Estimate | Standard Error |
Chi-Square | DF | Pr > ChiSq |
| 107 | DEC2008 | Additive Outlier | 4.17065 | 2.011465 | 4.30 | 1 | 0.0381 |
| 117 | OCT2009 | Additive Outlier | 4.06424 | 2.0088385 | 4.09 | 1 | 0.0431 |
| Forecasts for Variable incidents | |||||
|---|---|---|---|---|---|
| Obs | Date_of_death | Forecast | Standard Error |
95% Confidence Limits | |
| 238 | NOV2019 | 3.238375 | 2.01620 | -0.713297 | 7.190047 |
| 239 | DEC2019 | 2.342190 | 2.01632 | -1.609730 | 6.294111 |
| 240 | JAN2020 | 3.498637 | 2.01645 | -0.453529 | 7.450804 |
| 241 | FEB2020 | 3.588838 | 2.01441 | -0.359335 | 7.537011 |
| 242 | MAR2020 | 3.087462 | 2.01453 | -0.860953 | 7.035877 |
| 243 | APR2020 | 3.436087 | 2.01466 | -0.512568 | 7.384742 |
| 244 | MAY2020 | 3.334711 | 2.01478 | -0.614182 | 7.283604 |
| 245 | JUN2020 | 3.633334 | 2.01490 | -0.315795 | 7.582463 |
| 246 | JUL2020 | 2.731959 | 2.01502 | -1.217404 | 6.681322 |
| 247 | AUG2020 | 2.980584 | 2.01514 | -0.969011 | 6.930179 |
| 248 | SEP2020 | 2.779208 | 2.01525 | -1.170617 | 6.729033 |
| 249 | OCT2020 | 2.427833 | 2.01537 | -1.522221 | 6.377887 |
| Estimation Span Summary | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Variable | Type | First Obs | Last Obs | NObs | NMiss | Min | Max | Mean | Standard Deviation |
| incidents | Dependent | JAN2000 | SEP2019 | 237 | 0 | 1.00000 | 5.00000 | 3.13924 | 1.87129 |
| Forecast Span Summary | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Variable | Type | First Obs | Last Obs | NObs | NMiss | Min | Max | Mean | Standard Deviation |
| incidents | Dependent | JAN2000 | SEP2019 | 237 | 0 | 1.00000 | 5.00000 | 3.13924 | 1.87129 |
| Preliminary Estimates of the Free Parameters | ||
|---|---|---|
| Component | Parameter | Estimate |
| Irregular | Error Variance | 2.78955 |
| Level | Error Variance | 1.04608 |
| Season | Error Variance | 3.21531 |
| Likelihood Based Fit Statistics | |
|---|---|
| Statistic | Value |
| Full Log Likelihood | -474.9 |
| Diffuse Part of Log Likelihood | -2.485 |
| Non-Missing Observations Used | 237 |
| Estimated Parameters | 3 |
| Initialized Diffuse State Elements | 12 |
| Normalized Residual Sum of Squares | 225 |
| AIC (smaller is better) | 955.76 |
| BIC (smaller is better) | 966.01 |
| AICC (smaller is better) | 955.87 |
| HQIC (smaller is better) | 959.9 |
| CAIC (smaller is better) | 969.01 |
| Likelihood Optimization Algorithm Converged in 5 Iterations. |
| Final Estimates of the Free Parameters | |||||
|---|---|---|---|---|---|
| Component | Parameter | Estimate | Approx Std Error |
t Value | Approx Pr > |t| |
| Irregular | Error Variance | 3.11062 | 0.33246 | 9.36 | <.0001 |
| Level | Error Variance | 0.00990 | 0.01322 | 0.75 | 0.4539 |
| Season | Error Variance | 0.01150 | 0.01634 | 0.70 | 0.4814 |
| Fit Statistics Based on Residuals | |
|---|---|
| Number of non-missing residuals used for computing the fit statistics = 225 | |
| Mean Squared Error | 3.91976 |
| Root Mean Squared Error | 1.97984 |
| Mean Absolute Percentage Error | 98.83590 |
| Maximum Percent Error | 80.00000 |
| R-Square | -0.13177 |
| Adjusted R-Square | -0.14197 |
| Random Walk R-Square | 0.33384 |
| Amemiya's Adjusted R-Square | -0.16236 |
| Significance Analysis of Components (Based on the Final State) | |||
|---|---|---|---|
| Component | DF | Chi-Square | Pr > ChiSq |
| Irregular | 1 | 5.38 | 0.0204 |
| Level | 1 | 34.78 | <.0001 |
| Season | 11 | 6.50 | 0.8382 |
| Trend Information (Based on the Final State) | ||
|---|---|---|
| Name | Estimate | Standard Error |
| Level | 2.441238724 | 0.4139205 |
| Summary of Seasons | |||
|---|---|---|---|
| Name | Type | Season Length | Error Variance |
| Season | DUMMY | 12 | 0.01150 |
| Forecasts for Variable incidents | |||||
|---|---|---|---|---|---|
| Obs | Date_of_death | Forecast | Standard Error |
95% Confidence Limits | |
| 238 | OCT2019 | 2.688823 | 1.89341 | -1.022193 | 6.399838 |
| 239 | NOV2019 | 2.785220 | 1.89441 | -0.927756 | 6.498196 |
| 240 | DEC2019 | 1.899534 | 1.89661 | -1.817759 | 5.616826 |
| 241 | JAN2020 | 2.127988 | 1.89807 | -1.592155 | 5.848130 |
| 242 | FEB2020 | 1.954924 | 1.90033 | -1.769651 | 5.679499 |
| 243 | MAR2020 | 2.872513 | 1.90257 | -0.856448 | 6.601475 |
| 244 | APR2020 | 1.999811 | 1.90478 | -1.733485 | 5.733107 |
| 245 | MAY2020 | 2.457661 | 1.90697 | -1.279927 | 6.195249 |
| 246 | JUN2020 | 2.534700 | 1.90914 | -1.207138 | 6.276537 |
| 247 | JUL2020 | 2.367244 | 1.91127 | -1.378782 | 6.113269 |
| 248 | AUG2020 | 3.118175 | 1.91329 | -0.631808 | 6.868159 |
| 249 | SEP2020 | 2.488273 | 1.91419 | -1.263462 | 6.240009 |
| Estimation Span Summary | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Variable | Type | First Obs | Last Obs | NObs | NMiss | Min | Max | Mean | Standard Deviation |
| incidents | Dependent | JAN2000 | SEP2019 | 237 | 0 | 1.00000 | 5.00000 | 3.29536 | 1.87459 |
| Forecast Span Summary | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Variable | Type | First Obs | Last Obs | NObs | NMiss | Min | Max | Mean | Standard Deviation |
| incidents | Dependent | JAN2000 | SEP2019 | 237 | 0 | 1.00000 | 5.00000 | 3.29536 | 1.87459 |
| Preliminary Estimates of the Free Parameters | ||
|---|---|---|
| Component | Parameter | Estimate |
| Irregular | Error Variance | 2.79941 |
| Level | Error Variance | 1.04978 |
| Season | Error Variance | 3.42187 |
| Likelihood Based Fit Statistics | |
|---|---|
| Statistic | Value |
| Full Log Likelihood | -481.2 |
| Diffuse Part of Log Likelihood | -2.485 |
| Non-Missing Observations Used | 237 |
| Estimated Parameters | 3 |
| Initialized Diffuse State Elements | 12 |
| Normalized Residual Sum of Squares | 225 |
| AIC (smaller is better) | 968.43 |
| BIC (smaller is better) | 978.67 |
| AICC (smaller is better) | 968.53 |
| HQIC (smaller is better) | 972.56 |
| CAIC (smaller is better) | 981.67 |
| Likelihood Optimization Algorithm Converged in 14 Iterations. |
| Final Estimates of the Free Parameters | |||||
|---|---|---|---|---|---|
| Component | Parameter | Estimate | Approx Std Error |
t Value | Approx Pr > |t| |
| Irregular | Error Variance | 3.45183 | 0.34436 | 10.02 | <.0001 |
| Level | Error Variance | 1.979545E-9 | 1.33779E-6 | 0.00 | 0.9988 |
| Season | Error Variance | 0.01079 | 0.01949 | 0.55 | 0.5799 |
| Fit Statistics Based on Residuals | |
|---|---|
| Number of non-missing residuals used for computing the fit statistics = 225 | |
| Mean Squared Error | 4.12791 |
| Root Mean Squared Error | 2.03173 |
| Mean Absolute Percentage Error | 98.77465 |
| Maximum Percent Error | 80.14496 |
| R-Square | -0.18491 |
| Adjusted R-Square | -0.19559 |
| Random Walk R-Square | 0.39096 |
| Amemiya's Adjusted R-Square | -0.21693 |
| Significance Analysis of Components (Based on the Final State) | |||
|---|---|---|---|
| Component | DF | Chi-Square | Pr > ChiSq |
| Irregular | 1 | 12.25 | 0.0005 |
| Level | 1 | 743.34 | <.0001 |
| Season | 11 | 6.11 | 0.8661 |
| Trend Information (Based on the Final State) | ||
|---|---|---|
| Name | Estimate | Standard Error |
| Level | 3.291449974 | 0.1207239 |
| Summary of Seasons | |||
|---|---|---|---|
| Name | Type | Season Length | Error Variance |
| Season | DUMMY | 12 | 0.01079 |
| Forecasts for Variable incidents | |||||
|---|---|---|---|---|---|
| Obs | Date_of_death | Forecast | Standard Error |
95% Confidence Limits | |
| 238 | OCT2019 | 3.244927 | 1.93841 | -0.554277 | 7.044131 |
| 239 | NOV2019 | 3.012830 | 1.93865 | -0.786845 | 6.812506 |
| 240 | DEC2019 | 2.880465 | 1.93861 | -0.919148 | 6.680077 |
| 241 | JAN2020 | 3.604917 | 1.93740 | -0.192308 | 7.402143 |
| 242 | FEB2020 | 4.039041 | 1.93736 | 0.241892 | 7.836191 |
| 243 | MAR2020 | 3.745257 | 1.93736 | -0.051891 | 7.542405 |
| 244 | APR2020 | 3.138589 | 1.93736 | -0.658559 | 6.935737 |
| 245 | MAY2020 | 3.380387 | 1.93736 | -0.416761 | 7.177535 |
| 246 | JUN2020 | 3.332220 | 1.93736 | -0.464928 | 7.129368 |
| 247 | JUL2020 | 3.023305 | 1.93736 | -0.773843 | 6.820453 |
| 248 | AUG2020 | 3.241055 | 1.93736 | -0.556094 | 7.038205 |
| 249 | SEP2020 | 2.854405 | 1.93756 | -0.943143 | 6.651953 |
| Estimation Span Summary | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Variable | Type | First Obs | Last Obs | NObs | NMiss | Min | Max | Mean | Standard Deviation |
| incidents | Dependent | FEB2000 | SEP2019 | 236 | 0 | 1.00000 | 6.00000 | 2.59746 | 1.82973 |
| Forecast Span Summary | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Variable | Type | First Obs | Last Obs | NObs | NMiss | Min | Max | Mean | Standard Deviation |
| incidents | Dependent | FEB2000 | SEP2019 | 236 | 0 | 1.00000 | 6.00000 | 2.59746 | 1.82973 |
| Preliminary Estimates of the Free Parameters | ||
|---|---|---|
| Component | Parameter | Estimate |
| Irregular | Error Variance | 2.66698 |
| Level | Error Variance | 1.00012 |
| Season | Error Variance | 3.19053 |
| Likelihood Based Fit Statistics | |
|---|---|
| Statistic | Value |
| Full Log Likelihood | -472.6 |
| Diffuse Part of Log Likelihood | -2.485 |
| Non-Missing Observations Used | 236 |
| Estimated Parameters | 3 |
| Initialized Diffuse State Elements | 12 |
| Normalized Residual Sum of Squares | 224 |
| AIC (smaller is better) | 951.16 |
| BIC (smaller is better) | 961.4 |
| AICC (smaller is better) | 951.27 |
| HQIC (smaller is better) | 955.29 |
| CAIC (smaller is better) | 964.4 |
| Likelihood Optimization Algorithm Converged in 7 Iterations. |
| Final Estimates of the Free Parameters | |||||
|---|---|---|---|---|---|
| Component | Parameter | Estimate | Approx Std Error |
t Value | Approx Pr > |t| |
| Irregular | Error Variance | 3.25083 | 0.33011 | 9.85 | <.0001 |
| Level | Error Variance | 0.00245 | 0.0037309 | 0.66 | 0.5120 |
| Season | Error Variance | 0.00169 | 0.01503 | 0.11 | 0.9105 |
| Fit Statistics Based on Residuals | |
|---|---|
| Number of non-missing residuals used for computing the fit statistics = 224 | |
| Mean Squared Error | 4.09430 |
| Root Mean Squared Error | 2.02344 |
| Mean Absolute Percentage Error | 84.21610 |
| Maximum Percent Error | 83.18547 |
| R-Square | -0.24670 |
| Adjusted R-Square | -0.25799 |
| Random Walk R-Square | 0.35819 |
| Amemiya's Adjusted R-Square | -0.28055 |
| Significance Analysis of Components (Based on the Final State) | |||
|---|---|---|---|
| Component | DF | Chi-Square | Pr > ChiSq |
| Irregular | 1 | 0.10 | 0.7473 |
| Level | 1 | 99.94 | <.0001 |
| Season | 11 | 9.71 | 0.5567 |
| Trend Information (Based on the Final State) | ||
|---|---|---|
| Name | Estimate | Standard Error |
| Level | 2.967147943 | 0.2968094 |
| Summary of Seasons | |||
|---|---|---|---|
| Name | Type | Season Length | Error Variance |
| Season | DUMMY | 12 | 0.00169 |
| Outlier Summary | |||||||
|---|---|---|---|---|---|---|---|
| Obs | Date_of_death | Break Type | Estimate | Standard Error |
Chi-Square | DF | Pr > ChiSq |
| 55 | AUG2004 | Additive Outlier | 4.23819 | 1.8630817 | 5.17 | 1 | 0.0229 |
| 103 | AUG2008 | Additive Outlier | 4.21711 | 1.8610898 | 5.13 | 1 | 0.0235 |
| 141 | OCT2011 | Additive Outlier | 4.12340 | 1.8634283 | 4.90 | 1 | 0.0269 |
| Forecasts for Variable incidents | |||||
|---|---|---|---|---|---|
| Obs | Date_of_death | Forecast | Standard Error |
95% Confidence Limits | |
| 237 | OCT2019 | 2.602419 | 1.87745 | -1.077315 | 6.282154 |
| 238 | NOV2019 | 3.017078 | 1.87780 | -0.663334 | 6.697491 |
| 239 | DEC2019 | 2.462186 | 1.87826 | -1.219138 | 6.143510 |
| 240 | JAN2020 | 3.689849 | 1.87873 | 0.007605 | 7.372092 |
| 241 | FEB2020 | 2.272231 | 1.87751 | -1.407625 | 5.952088 |
| 242 | MAR2020 | 3.208346 | 1.87798 | -0.472421 | 6.889113 |
| 243 | APR2020 | 3.189913 | 1.87843 | -0.491737 | 6.871563 |
| 244 | MAY2020 | 3.100163 | 1.87887 | -0.582362 | 6.782689 |
| 245 | JUN2020 | 2.917598 | 1.87932 | -0.765795 | 6.600991 |
| 246 | JUL2020 | 3.422432 | 1.87976 | -0.261821 | 7.106686 |
| 247 | AUG2020 | 2.561581 | 1.88019 | -1.123521 | 6.246684 |
| 248 | SEP2020 | 3.161978 | 1.88051 | -0.523745 | 6.847700 |
| Estimation Span Summary | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Variable | Type | First Obs | Last Obs | NObs | NMiss | Min | Max | Mean | Standard Deviation |
| incidents | Dependent | FEB2000 | SEP2019 | 236 | 0 | 1.00000 | 4.00000 | 2.82627 | 1.33030 |
| Forecast Span Summary | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Variable | Type | First Obs | Last Obs | NObs | NMiss | Min | Max | Mean | Standard Deviation |
| incidents | Dependent | FEB2000 | SEP2019 | 236 | 0 | 1.00000 | 4.00000 | 2.82627 | 1.33030 |
| Preliminary Estimates of the Free Parameters | ||
|---|---|---|
| Component | Parameter | Estimate |
| Irregular | Error Variance | 1.40975 |
| Level | Error Variance | 0.52866 |
| Season | Error Variance | 1.69411 |
| Likelihood Based Fit Statistics | |
|---|---|
| Statistic | Value |
| Full Log Likelihood | -401.2 |
| Diffuse Part of Log Likelihood | -2.485 |
| Non-Missing Observations Used | 236 |
| Estimated Parameters | 3 |
| Initialized Diffuse State Elements | 12 |
| Normalized Residual Sum of Squares | 224 |
| AIC (smaller is better) | 808.33 |
| BIC (smaller is better) | 818.56 |
| AICC (smaller is better) | 808.44 |
| HQIC (smaller is better) | 812.46 |
| CAIC (smaller is better) | 821.56 |
| Likelihood Optimization Algorithm Converged in 14 Iterations. |
| Final Estimates of the Free Parameters | |||||
|---|---|---|---|---|---|
| Component | Parameter | Estimate | Approx Std Error |
t Value | Approx Pr > |t| |
| Irregular | Error Variance | 1.73891 | 0.19975 | 8.71 | <.0001 |
| Level | Error Variance | 1.189838E-9 | 8.18539E-7 | 0.00 | 0.9988 |
| Season | Error Variance | 0.00236 | 0.01798 | 0.13 | 0.8954 |
| Fit Statistics Based on Residuals | |
|---|---|
| Number of non-missing residuals used for computing the fit statistics = 224 | |
| Mean Squared Error | 2.05367 |
| Root Mean Squared Error | 1.43306 |
| Mean Absolute Percentage Error | 71.26681 |
| Maximum Percent Error | 74.99998 |
| R-Square | -0.17096 |
| Adjusted R-Square | -0.18156 |
| Random Walk R-Square | 0.41396 |
| Amemiya's Adjusted R-Square | -0.20275 |
| Significance Analysis of Components (Based on the Final State) | |||
|---|---|---|---|
| Component | DF | Chi-Square | Pr > ChiSq |
| Irregular | 1 | 15.11 | 0.0001 |
| Level | 1 | 1086.48 | <.0001 |
| Season | 11 | 11.17 | 0.4292 |
| Trend Information (Based on the Final State) | ||
|---|---|---|
| Name | Estimate | Standard Error |
| Level | 2.830339579 | 0.0858673 |
| Summary of Seasons | |||
|---|---|---|---|
| Name | Type | Season Length | Error Variance |
| Season | DUMMY | 12 | 0.00236 |
| Outlier Summary | |||||||
|---|---|---|---|---|---|---|---|
| Obs | Date_of_death | Break Type | Estimate | Standard Error |
Chi-Square | DF | Pr > ChiSq |
| 143 | DEC2011 | Additive Outlier | -2.71367 | 1.3581463 | 3.99 | 1 | 0.0457 |
| 107 | DEC2008 | Additive Outlier | -2.70681 | 1.3578992 | 3.97 | 1 | 0.0462 |
| Forecasts for Variable incidents | |||||
|---|---|---|---|---|---|
| Obs | Date_of_death | Forecast | Standard Error |
95% Confidence Limits | |
| 237 | OCT2019 | 2.867325 | 1.36387 | 0.194194 | 5.540456 |
| 238 | NOV2019 | 3.067848 | 1.36391 | 0.394635 | 5.741061 |
| 239 | DEC2019 | 3.600698 | 1.36391 | 0.927485 | 6.273910 |
| 240 | JAN2020 | 2.643969 | 1.36390 | -0.029229 | 5.317168 |
| 241 | FEB2020 | 2.991721 | 1.36268 | 0.320923 | 5.662518 |
| 242 | MAR2020 | 2.610620 | 1.36267 | -0.060160 | 5.281400 |
| 243 | APR2020 | 2.885889 | 1.36267 | 0.215108 | 5.556669 |
| 244 | MAY2020 | 2.542144 | 1.36267 | -0.128636 | 5.212924 |
| 245 | JUN2020 | 3.137241 | 1.36267 | 0.466460 | 5.808021 |
| 246 | JUL2020 | 2.620623 | 1.36267 | -0.050157 | 5.291403 |
| 247 | AUG2020 | 2.687398 | 1.36267 | 0.016618 | 5.358178 |
| 248 | SEP2020 | 2.308600 | 1.36270 | -0.362251 | 4.979452 |
| Estimation Span Summary | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Variable | Type | First Obs | Last Obs | NObs | NMiss | Min | Max | Mean | Standard Deviation |
| incidents | Dependent | JAN2000 | SEP2019 | 237 | 0 | 1.00000 | 6.00000 | 3.33755 | 2.30603 |
| Forecast Span Summary | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Variable | Type | First Obs | Last Obs | NObs | NMiss | Min | Max | Mean | Standard Deviation |
| incidents | Dependent | JAN2000 | SEP2019 | 237 | 0 | 1.00000 | 6.00000 | 3.33755 | 2.30603 |
| Preliminary Estimates of the Free Parameters | ||
|---|---|---|
| Component | Parameter | Estimate |
| Irregular | Error Variance | 4.23627 |
| Level | Error Variance | 1.58860 |
| Season | Error Variance | 5.85033 |
| Likelihood Based Fit Statistics | |
|---|---|
| Statistic | Value |
| Full Log Likelihood | -527.9 |
| Diffuse Part of Log Likelihood | -2.485 |
| Non-Missing Observations Used | 237 |
| Estimated Parameters | 3 |
| Initialized Diffuse State Elements | 12 |
| Normalized Residual Sum of Squares | 225 |
| AIC (smaller is better) | 1061.9 |
| BIC (smaller is better) | 1072.1 |
| AICC (smaller is better) | 1062 |
| HQIC (smaller is better) | 1066 |
| CAIC (smaller is better) | 1075.1 |
| Likelihood Optimization Algorithm Converged in 13 Iterations. |
| Final Estimates of the Free Parameters | |||||
|---|---|---|---|---|---|
| Component | Parameter | Estimate | Approx Std Error |
t Value | Approx Pr > |t| |
| Irregular | Error Variance | 5.26204 | 0.50077 | 10.51 | <.0001 |
| Level | Error Variance | 0.00267 | 0.0035726 | 0.75 | 0.4547 |
| Season | Error Variance | 1.270137E-7 | 0.00006925 | 0.00 | 0.9985 |
| Fit Statistics Based on Residuals | |
|---|---|
| Number of non-missing residuals used for computing the fit statistics = 225 | |
| Mean Squared Error | 6.42556 |
| Root Mean Squared Error | 2.53487 |
| Mean Absolute Percentage Error | 131.16827 |
| Maximum Percent Error | 83.97269 |
| R-Square | -0.22959 |
| Adjusted R-Square | -0.24067 |
| Random Walk R-Square | 0.21933 |
| Amemiya's Adjusted R-Square | -0.26283 |
| Significance Analysis of Components (Based on the Final State) | |||
|---|---|---|---|
| Component | DF | Chi-Square | Pr > ChiSq |
| Irregular | 1 | 2.93 | 0.0869 |
| Level | 1 | 68.58 | <.0001 |
| Season | 11 | 7.81 | 0.7298 |
| Trend Information (Based on the Final State) | ||
|---|---|---|
| Name | Estimate | Standard Error |
| Level | 2.837076125 | 0.3425861 |
| Summary of Seasons | |||
|---|---|---|---|
| Name | Type | Season Length | Error Variance |
| Season | DUMMY | 12 | 1.270137E-7 |
| Forecasts for Variable incidents | |||||
|---|---|---|---|---|---|
| Obs | Date_of_death | Forecast | Standard Error |
95% Confidence Limits | |
| 238 | OCT2019 | 2.127864 | 2.37503 | -2.527111 | 6.782840 |
| 239 | NOV2019 | 3.026517 | 2.37540 | -1.629181 | 7.682216 |
| 240 | DEC2019 | 2.714638 | 2.37577 | -1.941777 | 7.371053 |
| 241 | JAN2020 | 2.638005 | 2.37365 | -2.014255 | 7.290265 |
| 242 | FEB2020 | 2.541720 | 2.37401 | -2.111244 | 7.194684 |
| 243 | MAR2020 | 2.445437 | 2.37436 | -2.208226 | 7.099100 |
| 244 | APR2020 | 2.899160 | 2.37471 | -1.755196 | 7.553515 |
| 245 | MAY2020 | 3.602876 | 2.37507 | -1.052167 | 8.257919 |
| 246 | JUN2020 | 3.256597 | 2.37541 | -1.399127 | 7.912321 |
| 247 | JUL2020 | 3.360312 | 2.37576 | -1.296087 | 8.016712 |
| 248 | AUG2020 | 2.414035 | 2.37610 | -2.243034 | 7.071104 |
| 249 | SEP2020 | 3.017751 | 2.37644 | -1.639982 | 7.675484 |
| Estimation Span Summary | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Variable | Type | First Obs | Last Obs | NObs | NMiss | Min | Max | Mean | Standard Deviation |
| incidents | Dependent | JAN2000 | OCT2019 | 238 | 0 | 1.00000 | 10.00000 | 3.80672 | 2.10796 |
| Forecast Span Summary | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Variable | Type | First Obs | Last Obs | NObs | NMiss | Min | Max | Mean | Standard Deviation |
| incidents | Dependent | JAN2000 | OCT2019 | 238 | 0 | 1.00000 | 10.00000 | 3.80672 | 2.10796 |
| Preliminary Estimates of the Free Parameters | ||
|---|---|---|
| Component | Parameter | Estimate |
| Irregular | Error Variance | 3.53986 |
| Level | Error Variance | 1.32745 |
| Season | Error Variance | 4.14160 |
| Likelihood Based Fit Statistics | |
|---|---|
| Statistic | Value |
| Full Log Likelihood | -509.6 |
| Diffuse Part of Log Likelihood | -2.485 |
| Non-Missing Observations Used | 238 |
| Estimated Parameters | 3 |
| Initialized Diffuse State Elements | 12 |
| Normalized Residual Sum of Squares | 226 |
| AIC (smaller is better) | 1025.3 |
| BIC (smaller is better) | 1035.5 |
| AICC (smaller is better) | 1025.4 |
| HQIC (smaller is better) | 1029.4 |
| CAIC (smaller is better) | 1038.5 |
| Likelihood Optimization Algorithm Converged in 13 Iterations. |
| Final Estimates of the Free Parameters | |||||
|---|---|---|---|---|---|
| Component | Parameter | Estimate | Approx Std Error |
t Value | Approx Pr > |t| |
| Irregular | Error Variance | 4.37697 | 0.42071 | 10.40 | <.0001 |
| Level | Error Variance | 0.00270 | 0.0048735 | 0.55 | 0.5796 |
| Season | Error Variance | 4.166321E-7 | 0.0002095 | 0.00 | 0.9984 |
| Fit Statistics Based on Residuals | |
|---|---|
| Number of non-missing residuals used for computing the fit statistics = 226 | |
| Mean Squared Error | 5.37843 |
| Root Mean Squared Error | 2.31914 |
| Mean Absolute Percentage Error | 67.88967 |
| Maximum Percent Error | 80.56736 |
| R-Square | -0.25985 |
| Adjusted R-Square | -0.27115 |
| Random Walk R-Square | 0.37494 |
| Amemiya's Adjusted R-Square | -0.29375 |
| Significance Analysis of Components (Based on the Final State) | |||
|---|---|---|---|
| Component | DF | Chi-Square | Pr > ChiSq |
| Irregular | 1 | 8.69 | 0.0032 |
| Level | 1 | 122.42 | <.0001 |
| Season | 11 | 10.43 | 0.4921 |
| Trend Information (Based on the Final State) | ||
|---|---|---|
| Name | Estimate | Standard Error |
| Level | 3.62765455 | 0.3278716 |
| Summary of Seasons | |||
|---|---|---|---|
| Name | Type | Season Length | Error Variance |
| Season | DUMMY | 12 | 4.166321E-7 |
| Outlier Summary | |||||||
|---|---|---|---|---|---|---|---|
| Obs | Date_of_death | Break Type | Estimate | Standard Error |
Chi-Square | DF | Pr > ChiSq |
| 12 | DEC2000 | Additive Outlier | 7.14669 | 2.1675592 | 10.87 | 1 | 0.0010 |
| 18 | JUN2001 | Additive Outlier | 6.75180 | 2.1617751 | 9.75 | 1 | 0.0018 |
| 167 | NOV2013 | Additive Outlier | 6.61972 | 2.1590547 | 9.40 | 1 | 0.0022 |
| Forecasts for Variable incidents | |||||
|---|---|---|---|---|---|
| Obs | Date_of_death | Forecast | Standard Error |
95% Confidence Limits | |
| 239 | NOV2019 | 3.340109 | 2.16859 | -0.910244 | 7.590462 |
| 240 | DEC2019 | 3.392387 | 2.16902 | -0.858810 | 7.643585 |
| 241 | JAN2020 | 4.276440 | 2.16718 | 0.028844 | 8.524035 |
| 242 | FEB2020 | 4.076096 | 2.16760 | -0.172329 | 8.324521 |
| 243 | MAR2020 | 3.325779 | 2.16802 | -0.923468 | 7.575027 |
| 244 | APR2020 | 3.475431 | 2.16844 | -0.774632 | 7.725494 |
| 245 | MAY2020 | 3.675104 | 2.16885 | -0.575768 | 7.925976 |
| 246 | JUN2020 | 3.724771 | 2.16926 | -0.526903 | 7.976444 |
| 247 | JUL2020 | 4.224431 | 2.16967 | -0.028037 | 8.476900 |
| 248 | AUG2020 | 3.574111 | 2.17007 | -0.679146 | 7.827368 |
| 249 | SEP2020 | 3.823762 | 2.17047 | -0.430277 | 8.077800 |
| 250 | OCT2020 | 2.623434 | 2.17086 | -1.631378 | 6.878247 |
| Estimation Span Summary | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Variable | Type | First Obs | Last Obs | NObs | NMiss | Min | Max | Mean | Standard Deviation |
| incidents | Dependent | JAN2000 | SEP2019 | 237 | 0 | 1.00000 | 6.00000 | 3.21097 | 1.99730 |
| Forecast Span Summary | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Variable | Type | First Obs | Last Obs | NObs | NMiss | Min | Max | Mean | Standard Deviation |
| incidents | Dependent | JAN2000 | SEP2019 | 237 | 0 | 1.00000 | 6.00000 | 3.21097 | 1.99730 |
| Preliminary Estimates of the Free Parameters | ||
|---|---|---|
| Component | Parameter | Estimate |
| Irregular | Error Variance | 3.17790 |
| Level | Error Variance | 1.19171 |
| Season | Error Variance | 4.31048 |
| Likelihood Based Fit Statistics | |
|---|---|
| Statistic | Value |
| Full Log Likelihood | -493.3 |
| Diffuse Part of Log Likelihood | -2.485 |
| Non-Missing Observations Used | 237 |
| Estimated Parameters | 3 |
| Initialized Diffuse State Elements | 12 |
| Normalized Residual Sum of Squares | 225 |
| AIC (smaller is better) | 992.51 |
| BIC (smaller is better) | 1002.8 |
| AICC (smaller is better) | 992.62 |
| HQIC (smaller is better) | 996.65 |
| CAIC (smaller is better) | 1005.8 |
| Likelihood Optimization Algorithm Converged in 13 Iterations. |
| Final Estimates of the Free Parameters | |||||
|---|---|---|---|---|---|
| Component | Parameter | Estimate | Approx Std Error |
t Value | Approx Pr > |t| |
| Irregular | Error Variance | 3.91751 | 0.36935 | 10.61 | <.0001 |
| Level | Error Variance | 9.00954E-12 | 1.19382E-7 | 0.00 | 0.9999 |
| Season | Error Variance | 4.104797E-8 | 0.00002473 | 0.00 | 0.9987 |
| Fit Statistics Based on Residuals | |
|---|---|
| Number of non-missing residuals used for computing the fit statistics = 225 | |
| Mean Squared Error | 4.84952 |
| Root Mean Squared Error | 2.20216 |
| Mean Absolute Percentage Error | 96.29301 |
| Maximum Percent Error | 83.33333 |
| R-Square | -0.25483 |
| Adjusted R-Square | -0.26613 |
| Random Walk R-Square | 0.31112 |
| Amemiya's Adjusted R-Square | -0.28874 |
| Significance Analysis of Components (Based on the Final State) | |||
|---|---|---|---|
| Component | DF | Chi-Square | Pr > ChiSq |
| Irregular | 1 | 2.50 | 0.1137 |
| Level | 1 | 624.04 | <.0001 |
| Season | 11 | 15.32 | 0.1684 |
| Trend Information (Based on the Final State) | ||
|---|---|---|
| Name | Estimate | Standard Error |
| Level | 3.212499999 | 0.1285991 |
| Summary of Seasons | |||
|---|---|---|---|
| Name | Type | Season Length | Error Variance |
| Season | DUMMY | 12 | 4.104797E-8 |
| Forecasts for Variable incidents | |||||
|---|---|---|---|---|---|
| Obs | Date_of_death | Forecast | Standard Error |
95% Confidence Limits | |
| 238 | OCT2019 | 3.578947 | 2.03069 | -0.401129 | 7.559022 |
| 239 | NOV2019 | 2.842106 | 2.03069 | -1.137970 | 6.822181 |
| 240 | DEC2019 | 3.578947 | 2.03069 | -0.401128 | 7.559022 |
| 241 | JAN2020 | 2.900000 | 2.02815 | -1.075098 | 6.875097 |
| 242 | FEB2020 | 3.400001 | 2.02815 | -0.575096 | 7.375098 |
| 243 | MAR2020 | 3.950000 | 2.02815 | -0.025097 | 7.925097 |
| 244 | APR2020 | 2.350000 | 2.02815 | -1.625097 | 6.325097 |
| 245 | MAY2020 | 2.900001 | 2.02815 | -1.075097 | 6.875098 |
| 246 | JUN2020 | 3.650000 | 2.02815 | -0.325097 | 7.625097 |
| 247 | JUL2020 | 3.900000 | 2.02815 | -0.075097 | 7.875097 |
| 248 | AUG2020 | 2.800000 | 2.02815 | -1.175097 | 6.775097 |
| 249 | SEP2020 | 2.700000 | 2.02815 | -1.275097 | 6.675098 |
| Estimation Span Summary | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Variable | Type | First Obs | Last Obs | NObs | NMiss | Min | Max | Mean | Standard Deviation |
| incidents | Dependent | FEB2000 | SEP2019 | 236 | 0 | 1.00000 | 4.00000 | 2.74153 | 1.38876 |
| Forecast Span Summary | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Variable | Type | First Obs | Last Obs | NObs | NMiss | Min | Max | Mean | Standard Deviation |
| incidents | Dependent | FEB2000 | SEP2019 | 236 | 0 | 1.00000 | 4.00000 | 2.74153 | 1.38876 |
| Preliminary Estimates of the Free Parameters | ||
|---|---|---|
| Component | Parameter | Estimate |
| Irregular | Error Variance | 1.53638 |
| Level | Error Variance | 0.57614 |
| Season | Error Variance | 1.91055 |
| Likelihood Based Fit Statistics | |
|---|---|
| Statistic | Value |
| Full Log Likelihood | -412.8 |
| Diffuse Part of Log Likelihood | -2.485 |
| Non-Missing Observations Used | 236 |
| Estimated Parameters | 3 |
| Initialized Diffuse State Elements | 12 |
| Normalized Residual Sum of Squares | 224 |
| AIC (smaller is better) | 831.62 |
| BIC (smaller is better) | 841.85 |
| AICC (smaller is better) | 831.73 |
| HQIC (smaller is better) | 835.75 |
| CAIC (smaller is better) | 844.85 |
| Likelihood Optimization Algorithm Converged in 5 Iterations. |
| Final Estimates of the Free Parameters | |||||
|---|---|---|---|---|---|
| Component | Parameter | Estimate | Approx Std Error |
t Value | Approx Pr > |t| |
| Irregular | Error Variance | 1.82591 | 0.19266 | 9.48 | <.0001 |
| Level | Error Variance | 0.00058777 | 0.0008149 | 0.72 | 0.4707 |
| Season | Error Variance | 0.01887 | 0.01838 | 1.03 | 0.3044 |
| Fit Statistics Based on Residuals | |
|---|---|
| Number of non-missing residuals used for computing the fit statistics = 224 | |
| Mean Squared Error | 2.31705 |
| Root Mean Squared Error | 1.52219 |
| Mean Absolute Percentage Error | 83.43059 |
| Maximum Percent Error | 75.01162 |
| R-Square | -0.20783 |
| Adjusted R-Square | -0.21876 |
| Random Walk R-Square | 0.42900 |
| Amemiya's Adjusted R-Square | -0.24062 |
| Significance Analysis of Components (Based on the Final State) | |||
|---|---|---|---|
| Component | DF | Chi-Square | Pr > ChiSq |
| Irregular | 1 | 10.51 | 0.0012 |
| Level | 1 | 204.51 | <.0001 |
| Season | 11 | 5.40 | 0.9103 |
| Trend Information (Based on the Final State) | ||
|---|---|---|
| Name | Estimate | Standard Error |
| Level | 2.579651288 | 0.1803846 |
| Summary of Seasons | |||
|---|---|---|---|
| Name | Type | Season Length | Error Variance |
| Season | DUMMY | 12 | 0.01887 |
| Forecasts for Variable incidents | |||||
|---|---|---|---|---|---|
| Obs | Date_of_death | Forecast | Standard Error |
95% Confidence Limits | |
| 237 | OCT2019 | 2.107591 | 1.45650 | -0.747089 | 4.962271 |
| 238 | NOV2019 | 2.806151 | 1.45689 | -0.049310 | 5.661612 |
| 239 | DEC2019 | 1.948511 | 1.45696 | -0.907071 | 4.804094 |
| 240 | JAN2020 | 3.005117 | 1.45704 | 0.149373 | 5.860861 |
| 241 | FEB2020 | 2.479898 | 1.45692 | -0.375604 | 5.335400 |
| 242 | MAR2020 | 2.473575 | 1.45701 | -0.382103 | 5.329254 |
| 243 | APR2020 | 3.035188 | 1.45712 | 0.179279 | 5.891097 |
| 244 | MAY2020 | 2.138809 | 1.45723 | -0.717316 | 4.994935 |
| 245 | JUN2020 | 2.577580 | 1.45734 | -0.278750 | 5.433911 |
| 246 | JUL2020 | 2.767226 | 1.45743 | -0.089282 | 5.623733 |
| 247 | AUG2020 | 2.981255 | 1.45747 | 0.124671 | 5.837840 |
| 248 | SEP2020 | 2.634913 | 1.45775 | -0.222228 | 5.492054 |
| Estimation Span Summary | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Variable | Type | First Obs | Last Obs | NObs | NMiss | Min | Max | Mean | Standard Deviation |
| incidents | Dependent | JAN2000 | SEP2019 | 237 | 0 | 1.00000 | 4.00000 | 2.27848 | 1.27163 |
| Forecast Span Summary | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Variable | Type | First Obs | Last Obs | NObs | NMiss | Min | Max | Mean | Standard Deviation |
| incidents | Dependent | JAN2000 | SEP2019 | 237 | 0 | 1.00000 | 4.00000 | 2.27848 | 1.27163 |
| Preliminary Estimates of the Free Parameters | ||
|---|---|---|
| Component | Parameter | Estimate |
| Irregular | Error Variance | 1.28817 |
| Level | Error Variance | 0.48306 |
| Season | Error Variance | 1.68658 |
| Likelihood Based Fit Statistics | |
|---|---|
| Statistic | Value |
| Full Log Likelihood | -395 |
| Diffuse Part of Log Likelihood | -2.485 |
| Non-Missing Observations Used | 237 |
| Estimated Parameters | 3 |
| Initialized Diffuse State Elements | 12 |
| Normalized Residual Sum of Squares | 225 |
| AIC (smaller is better) | 796.02 |
| BIC (smaller is better) | 806.27 |
| AICC (smaller is better) | 796.13 |
| HQIC (smaller is better) | 800.16 |
| CAIC (smaller is better) | 809.27 |
| Likelihood Optimization Algorithm Converged in 11 Iterations. |
| Final Estimates of the Free Parameters | |||||
|---|---|---|---|---|---|
| Component | Parameter | Estimate | Approx Std Error |
t Value | Approx Pr > |t| |
| Irregular | Error Variance | 1.62883 | 0.16133 | 10.10 | <.0001 |
| Level | Error Variance | 0.00000563 | 0.0003533 | 0.02 | 0.9873 |
| Season | Error Variance | 0.00099787 | 0.0070562 | 0.14 | 0.8875 |
| Fit Statistics Based on Residuals | |
|---|---|
| Number of non-missing residuals used for computing the fit statistics = 225 | |
| Mean Squared Error | 1.96912 |
| Root Mean Squared Error | 1.40325 |
| Mean Absolute Percentage Error | 69.70696 |
| Maximum Percent Error | 75.01169 |
| R-Square | -0.24229 |
| Adjusted R-Square | -0.25348 |
| Random Walk R-Square | 0.36977 |
| Amemiya's Adjusted R-Square | -0.27587 |
| Significance Analysis of Components (Based on the Final State) | |||
|---|---|---|---|
| Component | DF | Chi-Square | Pr > ChiSq |
| Irregular | 1 | 0.00 | 0.9707 |
| Level | 1 | 711.85 | <.0001 |
| Season | 11 | 6.83 | 0.8126 |
| Trend Information (Based on the Final State) | ||
|---|---|---|
| Name | Estimate | Standard Error |
| Level | 2.281518542 | 0.0855126 |
| Summary of Seasons | |||
|---|---|---|---|
| Name | Type | Season Length | Error Variance |
| Season | DUMMY | 12 | 0.00099787 |
| Forecasts for Variable incidents | |||||
|---|---|---|---|---|---|
| Obs | Date_of_death | Forecast | Standard Error |
95% Confidence Limits | |
| 238 | OCT2019 | 2.102668 | 1.31458 | -0.473869 | 4.679205 |
| 239 | NOV2019 | 2.360532 | 1.31459 | -0.216021 | 4.937085 |
| 240 | DEC2019 | 2.556224 | 1.31459 | -0.020326 | 5.132774 |
| 241 | JAN2020 | 2.598955 | 1.31319 | 0.025145 | 5.172764 |
| 242 | FEB2020 | 2.011785 | 1.31319 | -0.562021 | 4.585591 |
| 243 | MAR2020 | 2.672603 | 1.31319 | 0.098797 | 5.246409 |
| 244 | APR2020 | 2.019861 | 1.31319 | -0.553946 | 4.593667 |
| 245 | MAY2020 | 2.297034 | 1.31319 | -0.276773 | 4.870840 |
| 246 | JUN2020 | 2.075046 | 1.31319 | -0.498760 | 4.648853 |
| 247 | JUL2020 | 2.261435 | 1.31319 | -0.312371 | 4.835242 |
| 248 | AUG2020 | 2.433314 | 1.31319 | -0.140493 | 5.007120 |
| 249 | SEP2020 | 1.988766 | 1.31320 | -0.585054 | 4.562587 |
| Estimation Span Summary | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Variable | Type | First Obs | Last Obs | NObs | NMiss | Min | Max | Mean | Standard Deviation |
| incidents | Dependent | JAN2000 | APR2019 | 232 | 0 | 1.00000 | 5.00000 | 3.32328 | 1.81475 |
| Forecast Span Summary | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Variable | Type | First Obs | Last Obs | NObs | NMiss | Min | Max | Mean | Standard Deviation |
| incidents | Dependent | JAN2000 | APR2019 | 232 | 0 | 1.00000 | 5.00000 | 3.32328 | 1.81475 |
| Preliminary Estimates of the Free Parameters | ||
|---|---|---|
| Component | Parameter | Estimate |
| Irregular | Error Variance | 2.62329 |
| Level | Error Variance | 0.98373 |
| Season | Error Variance | 3.34087 |
| Likelihood Based Fit Statistics | |
|---|---|
| Statistic | Value |
| Full Log Likelihood | -462.1 |
| Diffuse Part of Log Likelihood | -2.485 |
| Non-Missing Observations Used | 232 |
| Estimated Parameters | 3 |
| Initialized Diffuse State Elements | 12 |
| Normalized Residual Sum of Squares | 220 |
| AIC (smaller is better) | 930.2 |
| BIC (smaller is better) | 940.38 |
| AICC (smaller is better) | 930.31 |
| HQIC (smaller is better) | 934.31 |
| CAIC (smaller is better) | 943.38 |
| Likelihood Optimization Algorithm Converged in 13 Iterations. |
| Final Estimates of the Free Parameters | |||||
|---|---|---|---|---|---|
| Component | Parameter | Estimate | Approx Std Error |
t Value | Approx Pr > |t| |
| Irregular | Error Variance | 3.12513 | 0.30501 | 10.25 | <.0001 |
| Level | Error Variance | 0.00819 | 0.0068290 | 1.20 | 0.2302 |
| Season | Error Variance | 1.104823E-7 | 0.00006733 | 0.00 | 0.9987 |
| Fit Statistics Based on Residuals | |
|---|---|
| Number of non-missing residuals used for computing the fit statistics = 220 | |
| Mean Squared Error | 3.90958 |
| Root Mean Squared Error | 1.97727 |
| Mean Absolute Percentage Error | 97.13664 |
| Maximum Percent Error | 81.43832 |
| R-Square | -0.19042 |
| Adjusted R-Square | -0.20139 |
| Random Walk R-Square | 0.37123 |
| Amemiya's Adjusted R-Square | -0.22333 |
| Significance Analysis of Components (Based on the Final State) | |||
|---|---|---|---|
| Component | DF | Chi-Square | Pr > ChiSq |
| Irregular | 1 | 27.52 | <.0001 |
| Level | 1 | 93.64 | <.0001 |
| Season | 11 | 6.80 | 0.8149 |
| Trend Information (Based on the Final State) | ||
|---|---|---|
| Name | Estimate | Standard Error |
| Level | 3.826927089 | 0.3954652 |
| Summary of Seasons | |||
|---|---|---|---|
| Name | Type | Season Length | Error Variance |
| Season | DUMMY | 12 | 1.104823E-7 |
| Forecasts for Variable incidents | |||||
|---|---|---|---|---|---|
| Obs | Date_of_death | Forecast | Standard Error |
95% Confidence Limits | |
| 233 | MAY2019 | 3.618017 | 1.85681 | -0.021270 | 7.257305 |
| 234 | JUN2019 | 4.249396 | 1.85873 | 0.606356 | 7.892436 |
| 235 | JUL2019 | 3.512356 | 1.86062 | -0.134400 | 7.159112 |
| 236 | AUG2019 | 3.564787 | 1.86250 | -0.085651 | 7.215224 |
| 237 | SEP2019 | 4.090905 | 1.86436 | 0.436823 | 7.744988 |
| 238 | OCT2019 | 4.511758 | 1.86620 | 0.854066 | 8.169450 |
| 239 | NOV2019 | 3.616824 | 1.86803 | -0.044442 | 7.278090 |
| 240 | DEC2019 | 3.458723 | 1.86983 | -0.206082 | 7.123527 |
| 241 | JAN2020 | 3.837875 | 1.86981 | 0.173106 | 7.502645 |
| 242 | FEB2020 | 3.887684 | 1.87159 | 0.219436 | 7.555932 |
| 243 | MAR2020 | 3.737496 | 1.87335 | 0.065802 | 7.409190 |
| 244 | APR2020 | 3.837303 | 1.87509 | 0.162195 | 7.512411 |
| Estimation Span Summary | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Variable | Type | First Obs | Last Obs | NObs | NMiss | Min | Max | Mean | Standard Deviation |
| incidents | Dependent | JAN2000 | AUG2019 | 236 | 0 | 1.00000 | 5.00000 | 3.11441 | 1.82408 |
| Forecast Span Summary | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Variable | Type | First Obs | Last Obs | NObs | NMiss | Min | Max | Mean | Standard Deviation |
| incidents | Dependent | JAN2000 | AUG2019 | 236 | 0 | 1.00000 | 5.00000 | 3.11441 | 1.82408 |
| Preliminary Estimates of the Free Parameters | ||
|---|---|---|
| Component | Parameter | Estimate |
| Irregular | Error Variance | 2.65055 |
| Level | Error Variance | 0.99395 |
| Season | Error Variance | 3.18303 |
| Likelihood Based Fit Statistics | |
|---|---|
| Statistic | Value |
| Full Log Likelihood | -472.2 |
| Diffuse Part of Log Likelihood | -2.485 |
| Non-Missing Observations Used | 236 |
| Estimated Parameters | 3 |
| Initialized Diffuse State Elements | 12 |
| Normalized Residual Sum of Squares | 224 |
| AIC (smaller is better) | 950.42 |
| BIC (smaller is better) | 960.65 |
| AICC (smaller is better) | 950.53 |
| HQIC (smaller is better) | 954.55 |
| CAIC (smaller is better) | 963.65 |
| Likelihood Optimization Algorithm Converged in 6 Iterations. |
| Final Estimates of the Free Parameters | |||||
|---|---|---|---|---|---|
| Component | Parameter | Estimate | Approx Std Error |
t Value | Approx Pr > |t| |
| Irregular | Error Variance | 3.24934 | 0.32648 | 9.95 | <.0001 |
| Level | Error Variance | 0.00036260 | 0.0015178 | 0.24 | 0.8112 |
| Season | Error Variance | 0.00720 | 0.01624 | 0.44 | 0.6573 |
| Fit Statistics Based on Residuals | |
|---|---|
| Number of non-missing residuals used for computing the fit statistics = 224 | |
| Mean Squared Error | 3.95357 |
| Root Mean Squared Error | 1.98836 |
| Mean Absolute Percentage Error | 101.40380 |
| Maximum Percent Error | 80.23203 |
| R-Square | -0.19910 |
| Adjusted R-Square | -0.20995 |
| Random Walk R-Square | 0.31135 |
| Amemiya's Adjusted R-Square | -0.23166 |
| Significance Analysis of Components (Based on the Final State) | |||
|---|---|---|---|
| Component | DF | Chi-Square | Pr > ChiSq |
| Irregular | 1 | 3.63 | 0.0566 |
| Level | 1 | 261.59 | <.0001 |
| Season | 11 | 8.98 | 0.6233 |
| Trend Information (Based on the Final State) | ||
|---|---|---|
| Name | Estimate | Standard Error |
| Level | 3.010350438 | 0.1861262 |
| Summary of Seasons | |||
|---|---|---|---|
| Name | Type | Season Length | Error Variance |
| Season | DUMMY | 12 | 0.00720 |
| Forecasts for Variable incidents | |||||
|---|---|---|---|---|---|
| Obs | Date_of_death | Forecast | Standard Error |
95% Confidence Limits | |
| 237 | SEP2019 | 3.300403 | 1.87867 | -0.381722 | 6.982528 |
| 238 | OCT2019 | 2.841926 | 1.87869 | -0.840246 | 6.524098 |
| 239 | NOV2019 | 3.019040 | 1.87872 | -0.663187 | 6.701267 |
| 240 | DEC2019 | 2.538099 | 1.87875 | -1.144188 | 6.220386 |
| 241 | JAN2020 | 2.453930 | 1.87756 | -1.226013 | 6.133872 |
| 242 | FEB2020 | 2.342031 | 1.87759 | -1.337970 | 6.022032 |
| 243 | MAR2020 | 3.402193 | 1.87762 | -0.277873 | 7.082258 |
| 244 | APR2020 | 3.256222 | 1.87765 | -0.423904 | 6.936348 |
| 245 | MAY2020 | 3.631803 | 1.87768 | -0.048383 | 7.311988 |
| 246 | JUN2020 | 3.336824 | 1.87771 | -0.343419 | 7.017068 |
| 247 | JUL2020 | 3.033733 | 1.87773 | -0.646558 | 6.714023 |
| 248 | AUG2020 | 2.968003 | 1.87775 | -0.712324 | 6.648329 |
| Estimation Span Summary | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Variable | Type | First Obs | Last Obs | NObs | NMiss | Min | Max | Mean | Standard Deviation |
| incidents | Dependent | JAN2000 | OCT2019 | 238 | 0 | 1.00000 | 4.00000 | 2.43277 | 1.33822 |
| Forecast Span Summary | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Variable | Type | First Obs | Last Obs | NObs | NMiss | Min | Max | Mean | Standard Deviation |
| incidents | Dependent | JAN2000 | OCT2019 | 238 | 0 | 1.00000 | 4.00000 | 2.43277 | 1.33822 |
| Preliminary Estimates of the Free Parameters | ||
|---|---|---|
| Component | Parameter | Estimate |
| Irregular | Error Variance | 1.42664 |
| Level | Error Variance | 0.53499 |
| Season | Error Variance | 1.65660 |
| Likelihood Based Fit Statistics | |
|---|---|
| Statistic | Value |
| Full Log Likelihood | -403.6 |
| Diffuse Part of Log Likelihood | -2.485 |
| Non-Missing Observations Used | 238 |
| Estimated Parameters | 3 |
| Initialized Diffuse State Elements | 12 |
| Normalized Residual Sum of Squares | 226 |
| AIC (smaller is better) | 813.25 |
| BIC (smaller is better) | 823.51 |
| AICC (smaller is better) | 813.35 |
| HQIC (smaller is better) | 817.39 |
| CAIC (smaller is better) | 826.51 |
| Likelihood Optimization Algorithm Converged in 5 Iterations. |
| Final Estimates of the Free Parameters | |||||
|---|---|---|---|---|---|
| Component | Parameter | Estimate | Approx Std Error |
t Value | Approx Pr > |t| |
| Irregular | Error Variance | 1.65590 | 0.17204 | 9.63 | <.0001 |
| Level | Error Variance | 0.00328 | 0.0034844 | 0.94 | 0.3470 |
| Season | Error Variance | 0.00412 | 0.0099024 | 0.42 | 0.6773 |
| Fit Statistics Based on Residuals | |
|---|---|
| Number of non-missing residuals used for computing the fit statistics = 226 | |
| Mean Squared Error | 2.05104 |
| Root Mean Squared Error | 1.43214 |
| Mean Absolute Percentage Error | 73.80365 |
| Maximum Percent Error | 74.38476 |
| R-Square | -0.16651 |
| Adjusted R-Square | -0.17698 |
| Random Walk R-Square | 0.35441 |
| Amemiya's Adjusted R-Square | -0.19790 |
| Significance Analysis of Components (Based on the Final State) | |||
|---|---|---|---|
| Component | DF | Chi-Square | Pr > ChiSq |
| Irregular | 1 | 6.39 | 0.0115 |
| Level | 1 | 56.80 | <.0001 |
| Season | 11 | 10.81 | 0.4591 |
| Trend Information (Based on the Final State) | ||
|---|---|---|
| Name | Estimate | Standard Error |
| Level | 2.025889644 | 0.2688005 |
| Summary of Seasons | |||
|---|---|---|---|
| Name | Type | Season Length | Error Variance |
| Season | DUMMY | 12 | 0.00412 |
| Forecasts for Variable incidents | |||||
|---|---|---|---|---|---|
| Obs | Date_of_death | Forecast | Standard Error |
95% Confidence Limits | |
| 239 | NOV2019 | 2.154940 | 1.36573 | -0.521833 | 4.831714 |
| 240 | DEC2019 | 1.956273 | 1.36619 | -0.721405 | 4.633951 |
| 241 | JAN2020 | 1.779653 | 1.36641 | -0.898452 | 4.457758 |
| 242 | FEB2020 | 1.521184 | 1.36741 | -1.158888 | 4.201257 |
| 243 | MAR2020 | 1.597941 | 1.36840 | -1.084071 | 4.279953 |
| 244 | APR2020 | 1.926550 | 1.36938 | -0.757380 | 4.610479 |
| 245 | MAY2020 | 2.094934 | 1.37035 | -0.590895 | 4.780764 |
| 246 | JUN2020 | 2.331388 | 1.37131 | -0.356324 | 5.019101 |
| 247 | JUL2020 | 1.951307 | 1.37226 | -0.738271 | 4.640885 |
| 248 | AUG2020 | 2.241881 | 1.37320 | -0.449541 | 4.933303 |
| 249 | SEP2020 | 2.664584 | 1.37410 | -0.028604 | 5.357771 |
| 250 | OCT2020 | 2.090039 | 1.37452 | -0.603963 | 4.784042 |
| Estimation Span Summary | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Variable | Type | First Obs | Last Obs | NObs | NMiss | Min | Max | Mean | Standard Deviation |
| incidents | Dependent | JAN2000 | AUG2019 | 236 | 0 | 1.00000 | 4.00000 | 2.63559 | 1.33793 |
| Forecast Span Summary | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Variable | Type | First Obs | Last Obs | NObs | NMiss | Min | Max | Mean | Standard Deviation |
| incidents | Dependent | JAN2000 | AUG2019 | 236 | 0 | 1.00000 | 4.00000 | 2.63559 | 1.33793 |
| Preliminary Estimates of the Free Parameters | ||
|---|---|---|
| Component | Parameter | Estimate |
| Irregular | Error Variance | 1.42597 |
| Level | Error Variance | 0.53474 |
| Season | Error Variance | 1.89946 |
| Likelihood Based Fit Statistics | |
|---|---|
| Statistic | Value |
| Full Log Likelihood | -403.9 |
| Diffuse Part of Log Likelihood | -2.485 |
| Non-Missing Observations Used | 236 |
| Estimated Parameters | 3 |
| Initialized Diffuse State Elements | 12 |
| Normalized Residual Sum of Squares | 224 |
| AIC (smaller is better) | 813.71 |
| BIC (smaller is better) | 823.94 |
| AICC (smaller is better) | 813.82 |
| HQIC (smaller is better) | 817.84 |
| CAIC (smaller is better) | 826.94 |
| Likelihood Optimization Algorithm Converged in 13 Iterations. |
| Final Estimates of the Free Parameters | |||||
|---|---|---|---|---|---|
| Component | Parameter | Estimate | Approx Std Error |
t Value | Approx Pr > |t| |
| Irregular | Error Variance | 1.79717 | 0.16982 | 10.58 | <.0001 |
| Level | Error Variance | 1.858667E-9 | 1.04387E-6 | 0.00 | 0.9986 |
| Season | Error Variance | 2.816886E-8 | 0.00001952 | 0.00 | 0.9988 |
| Fit Statistics Based on Residuals | |
|---|---|
| Number of non-missing residuals used for computing the fit statistics = 224 | |
| Mean Squared Error | 2.14848 |
| Root Mean Squared Error | 1.46577 |
| Mean Absolute Percentage Error | 77.38853 |
| Maximum Percent Error | 75.00000 |
| R-Square | -0.20693 |
| Adjusted R-Square | -0.21786 |
| Random Walk R-Square | 0.42084 |
| Amemiya's Adjusted R-Square | -0.23970 |
| Significance Analysis of Components (Based on the Final State) | |||
|---|---|---|---|
| Component | DF | Chi-Square | Pr > ChiSq |
| Irregular | 1 | 28.49 | <.0001 |
| Level | 1 | 912.64 | <.0001 |
| Season | 11 | 10.07 | 0.5242 |
| Trend Information (Based on the Final State) | ||
|---|---|---|
| Name | Estimate | Standard Error |
| Level | 2.637061413 | 0.087291 |
| Summary of Seasons | |||
|---|---|---|---|
| Name | Type | Season Length | Error Variance |
| Season | DUMMY | 12 | 2.816886E-8 |
| Forecasts for Variable incidents | |||||
|---|---|---|---|---|---|
| Obs | Date_of_death | Forecast | Standard Error |
95% Confidence Limits | |
| 237 | SEP2019 | 2.631579 | 1.37541 | -0.064178 | 5.327336 |
| 238 | OCT2019 | 2.684212 | 1.37541 | -0.011545 | 5.379969 |
| 239 | NOV2019 | 2.315789 | 1.37541 | -0.379968 | 5.011546 |
| 240 | DEC2019 | 3.263158 | 1.37541 | 0.567401 | 5.958915 |
| 241 | JAN2020 | 3.050000 | 1.37369 | 0.357615 | 5.742385 |
| 242 | FEB2020 | 2.750001 | 1.37369 | 0.057615 | 5.442386 |
| 243 | MAR2020 | 2.500000 | 1.37369 | -0.192385 | 5.192385 |
| 244 | APR2020 | 2.499999 | 1.37369 | -0.192386 | 5.192385 |
| 245 | MAY2020 | 2.400000 | 1.37369 | -0.292385 | 5.092386 |
| 246 | JUN2020 | 2.250000 | 1.37369 | -0.442385 | 4.942385 |
| 247 | JUL2020 | 2.700000 | 1.37369 | 0.007615 | 5.392386 |
| 248 | AUG2020 | 2.599999 | 1.37369 | -0.092386 | 5.292385 |